Method of Initial Rates: Course Reader Question

[Rhiannon Imbeah 2I]

In the course under the section METHODS OF INITIAL RATES, the question was asked How does initial rate depend on the concentration of nitrogen dioxide [NO_{2 ?} What was the answer to this question?

[Christine_Mavilian_3E]

Based on what I gather from your question, in order to determine how the initial rate depends on [NO2-], you would have to calculate the order (n, m, variable used does not really matter) by using two experiments from a given data set. In order to do this you would use experiments one and two because the initial concentration of Ammonium is constant indicating that it would cancel out when you divide these values. Since rate=k[ ]^n[ ]^m you would set to solve the problem by dividing rate 2 by rate 1:

Rate 2: 2.70 x 10^-7mol. L^-1.s^-1= k ( 0.100 mol.L-1)^n (0.010 mol. L^-1)^m
divided by
Rate 1: 1.35 x 10^-7 mol. L^-1.s^-1 = k ( 0.100 mol.L-1)^n (0.005 mol. L^-1)^m

Since the concentrations of Ammonium cancel out as does k, you would divide the remaining values to obtain:

2= 2.0^m where m=1 because 2^1=2
Thus you can see that when the concentration of NO2- doubles from rate 1 to rate two, the rate also doubles.

I hope this helps!